Properties of Inverse Trigonometric Functions

The video tutorial covers the properties of inverse trigonometric functions, including reciprocal, even and odd, complementary, sum and difference, and double-angle formulas. It provides proofs and examples to illustrate these properties, helping students understand their applications in solving trigonometric equations.

What is the reciprocal relation for sine inverse in terms of cosecant inverse?

• sine inverse of x = cosec inverse 1/x

• sine inverse of 1/x = cosec inverse x

• sine inverse of 1/x = sec inverse x

• sine inverse of x = sec inverse 1/x

Which property is true for sine inverse of negative x?

• sine inverse of -x = 2pi + sine inverse x

• sine inverse of -x = pi - sine inverse x

• sine inverse of -x = -sine inverse x

• sine inverse of -x = sine inverse x

What is the property for cos inverse of negative x?

• cos inverse of -x = pi + cos inverse x

• cos inverse of -x = -cos inverse x

• cos inverse of -x = pi - cos inverse x

• cos inverse of -x = 2pi - cos inverse x

What is the complementary relation for sine inverse and cosine inverse?

• sine inverse x + cos inverse x = 2pi

• sine inverse x + cos inverse x = 0

• sine inverse x + cos inverse x = pi/2

• sine inverse x + cos inverse x = pi

What is the complementary relation for tan inverse x and cot inverse x?

• tan inverse x + cot inverse x = 0

• tan inverse x + cot inverse x = pi/2

• tan inverse x + cot inverse x = pi

• tan inverse x + cot inverse x = 2pi

What is the sum formula for tan inverse x and tan inverse y when xy < 1?

• tan inverse x + tan inverse y = tan inverse (x - y)/(1 + xy)

• tan inverse x + tan inverse y = tan inverse (x + y)/(1 - xy)

• tan inverse x + tan inverse y = tan inverse (x - y)/(1 - xy)

• tan inverse x + tan inverse y = tan inverse (x + y)/(1 + xy)

What is the double-angle formula for 2 times tan inverse x?

• 2 tan inverse x = sine inverse (2x)/(1 - x^2)

• 2 tan inverse x = cos inverse (2x)/(1 + x^2)

• 2 tan inverse x = tan inverse (2x)/(1 - x^2)

• 2 tan inverse x = tan inverse (2x)/(1 + x^2)

What is the result of 2 times sine inverse of 2x times the square root of 1 minus x squared?

• 2 times cos inverse x

• 2 times sine inverse x

• 4 times cos inverse x

• 4 times sine inverse x

What is the simplest form of cosec inverse of 1 over the square root of 1 minus x squared?

• tan inverse x

• sine inverse x

• cos inverse x

• cosec inverse x

What is the value of cos of tan inverse x plus cot inverse x?

• 1

• pi

• 0

• pi/2